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# On a certain sightseeing tour, the ratio of the number of

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On a certain sightseeing tour, the ratio of the number of [#permalink]  09 Dec 2005, 20:13
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On a certain sightseeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sightseeing tour?

(1) On the tour, the ratio of the number of children to the number of men was 5 to 11
(2) The number of women on the sightseeing tour was less than 30.

OPEN DISCUSSION OF THIS QUESTION IS HERE: on-a-certain-sight-seeing-tour-the-ratio-of-the-number-of-68645.html
[Reveal] Spoiler: OA
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Director
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Women:Children = 5:2

Statement1) Chidren:Men = 5:11

Women = 5x
Children = 2x

Children = 2x
Men = (22/5)x

(x and y are integers)

We do not know x, and so we do not know Men's number.

Insufficient.

Statement2) Women < 30

Women = 5x < 30

x < 6

x can be 1, 2, 3, 4, or 5.

Insufficient.

Statement 1 & 2)

From statement1, we know that men's number is (22/5)x.
Since the number of a group of people must be an integer, x should be a multiple of 5.
From statement2, x can be 1, 2, 3, 4, or 5, among which only 5 is a multiple of 5.

Therefore, x = 5.

Sufficient.
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Re: Sightseeing tour- DS [#permalink]  09 Dec 2005, 22:24
Jennif102 wrote:
On a certain sightseeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sightseeing tour?

1. On the tour, the ratio of the number of children to the number of men was 5 to 11
2. The number of women on the sightseeing tour was less than 30.

from 1 statement we can find out the whole ratio W to Child and Men alone insuf because we need not ratio but number
from statement 2 alone we dn't get anything

1 and 2 together do the job!My approuch to DS may be wrong but why to solve further if you already know that from 1 and 2 we can figure out the answer!IMHO
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Re: On a certain sightseeing tour, the ratio of the number of [#permalink]  15 Sep 2013, 09:18
(1) We are only given ratios and the question is asking for a number --> NOT SUFFICIENT

(2) We are given a range for the number of women, but do not know the ratio of women to men --> NOT SUFFICIENT

Combined:

We know that the ratio women:children = 5:2 and the ratio children:men = 5:11

Since "children" occur in both ratios, we can use them to directly compare the ratio of women to men (we want to find this ratio, because we are given a specific range for women in statement 2):

W:C = 5:2 = 25:10
C:M = 5:11 = 10:22
Combined ratio: W:C:M = 25:10:22

The number of men could be 22 or any multiple thereof. However, we are told that the number of women is below 30. The only multiple of 25 (ratio women) below 30 is 25, thus the number of men must also be 22. --> SUFFICIENT

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Re: On a certain sightseeing tour, the ratio of the number of [#permalink]  15 Sep 2013, 09:23
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Expert's post
On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?

Given: $$\frac{w}{c}=\frac{5}{2}$$ --> $$w=5x$$ and $$c=2x$$ for some integer $$x$$. Q: $$m=?$$

(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11 --> $$\frac{c}{m}=\frac{5}{11}$$ --> $$c=5y$$ and $$m=11y$$, for some integer $$y$$. Not sufficient to calculate $$m$$.

(2) The number of women on the sight-seeing tour was less than 30 --> $$w<30$$. Not sufficient to calculate $$m$$.

(1)+(2) $$w=5x<30$$ --> $$x<6$$. $$c=2x$$ and as $$c=5y$$, $$c$$ is a multiple of 5 --> $$x=5$$ --> $$c=10=5y$$ --> $$y=2$$ --> $$m=11y=22$$. Sufficient.

OR: $$\frac{\frac{w}{c}}{m}=\frac{\frac{25}{10}}{22}$$ --> $$\frac{w}{m}=\frac{25}{22}$$ and as $$w<30$$, then $$w=25$$ because for other values of $$w<30$$, $$m$$ (and $$c$$) are not integers --> $$m=22$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: on-a-certain-sight-seeing-tour-the-ratio-of-the-number-of-68645.html
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Re: On a certain sightseeing tour, the ratio of the number of   [#permalink] 15 Sep 2013, 09:23
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